CIE 1931 tristimulus values for reference white;

, surround white luminance;

, reproduced image white luminance;

, adapting luminance. If data on adapting luminance are not available it is recommended be taken to be equal to:

(4.26)

surround impact factor

chromatic induction factor

factor for degree of adaptation

relative luminance of the background. If the value of this parameter is unavailable it can be adopted to be equal to:

(4.27)

If data on , and are unavailable they can be chosen as follows.

Categorical viewing conditions settings for the model

Viewing condition

Average surround

0.69

1.0

1.0

Dim surround

0.59

0.9

0.9

Dark surround

0.525

0.8

0.8

Surround type may be defined via such a relationship:

(4.28)

The value corresponds to dark surround, to dim one and to average one.

The cone responses are:

(4.29)

here

(4.30)

The degree of viewers adaptation:

(4.31)

The adaptation transform is:

(4.32)

(4.33)

(4.34)

(4.35)

(4.36)

(4.37)

The transformation to Hunt-Pointer-Estevez cone responses is conducted as follows

(4.38)

(4.39)

(4.40)

The nonlinear response compression transform is:

(4.41)

If any of values of are negative then their absolute values are used and then the corresponding quotient term in Equations (4.41) must be multiplied by a negative 1 before adding the value 0.1.

Opponent axes:

(4.42)

Hue angle:

(4.43)

(4.44)

(4.45)

Eccentricity factor:

(4.46)

Color quadrature may be obtained via linear interpolation method:

(4.47)

using the values of unique hues shown in Table below. Here if , and else wise.

Unique hue data for the calculation of hue quadrature

Red

Yellow

Green

Blue

Red

20.14

90.00

164.25

237.53

380.14

0.8

0.7

1.0

1.2

0.8

0.0

100.0

200.0

300.0

400.0

The achromatic response is:

(4.48)

The lightness is:

(4.49)

The brightness is:

(4.50)

The chroma is:

(4.51)

here

(4.52)

The colorfulness is:

(4.53)

The saturation is:

. (4.54)

CIECAM02 includes three attributes in relation to the chromatic content: chroma (C), colorfulness (M) and saturation (s). These attributes together with lightness (J) and hue angle (h) can form three colour spaces , where

CIECAM02 chromaticity diagram

CIECAM02 chromaticity diagram is presented in Figures 4.1, 4.2 and 4.3 [4.6]. The figures demonstrate the dependence of colour appearance on adaptation level L_{A} and relative luminance level Y. It is seen from this figures that a variation of adapting luminance level may lead to significant colorfulness variation, and that variation of colorfulness increases with stimulus relative luminance growth.

Inverse conversion equations

First its necessary to compute surround-dependent parameters and achromatic response for reference white by using forward conversion. Lightness value can be obtained from brightness by using the following equation:

(4.55)

The chroma is:

(4.56)

If starting from lightness, the brightness can be calculated:

(4.57)

If saturation is known the chroma is defined as follows:

(4.58)

If hue quadrature data is available the hue angle can be calculated using unique hue data for the calculation of hue quadrature as:

(4.59)

here , if , otherwise

(4.60)

The eccentricity factor is:

(4.61)

The achromatic response is:

(4.62)

The following relationships are used for obtaining and values:

(4.63)

(4.64)

(4.65)

(4.66)

if , then:

(4.67)

(4.68)

(4.69)

if , then:

(4.70)

(4.71)

(4.72)

The cone responses are:

(4.73)

(4.74)

If any of the values of are negative, then the corresponding value must be negative.